Dr Y zhou Lecture notes 2005 Groundwater Hydraulics W)X h h K L h2=h2-( L UNESCO-IHE institute for Water Education
Dr Y Zhou Lecture Notes 2005 Groundwater Hydraulics w 0 L x h h0 K hL x w)x x+)x x K w )x - K wL - L h - h h = h -( L 2 2 0 2 0 2 2
Table of Contents 1. Introduction l. 1 Hydrological Cycle…… 2 Aquifer systems 1. 2. 1 Aquifer, aquitard, and aquiclude 1.2.2 uifer type 1.3 Vertical distribution of groundwater 33346 1. 4 Groundwater flow systems 2. Fundamental Equations of groundwater Flow. 2.1 2.2 Generalization of Darcy's Law 2.3 Equation of continuity 2.4 Basic equations for steady incompressible flow 3578 2.5 Basic equations for non-steady compressible flow Steady groundwater Flow in Aquifers 3.1 Groundwater flow in a confined aquifer. 3.1 Conceptual hydrogeological model 3.1.2 Mathematical model 3.1.3 Analytical solution 3.1.4 3.2 Groundwater Flow in an Unconfined Aquifer. 3.2. 1 Conceptual hydrogeological model 3.2.2 Mathematical model 3.2.3 Analytical solution 3.2.4 Analysis of solution 3.3 Groundwater flow in a semi-confined aquifer. 3.3.1 Conceptual hydrogeological model 3.3.2 Mathematical model 778922234 3.3.3 Analytical solution 3.3.4 Analysis of result 4. Steady Groundwater Flow to Wells 4.1 Groundwater flow to a well in a confined aquifer. 4.1.1 Conceptual hydrogeological model.. 4.1.2 Mathematical model 4. 1.3 Analytical solution 4.1.4 Analysis of results 4.1.5 Application to pumping test 4.2 Groundwater flow to a well in an unconfined aquifer hydrogeological model 4.2.2 Mathematical model 4.2.3 4.2.4 Analysis of results 4.2.5 Application to pumping test 4.3 Groundwater flow to a well in a semi-confined aquifer. hydrogeological mo 4.3.2 Mathematical model
Table of Contents 1. Introduction...............................................................................................................................................1 1.1 Hydrological Cycle ...........................................................................................................................1 1.2 Aquifer systems................................................................................................................................3 1.2.1 Aquifer, aquitard, and aquiclude ................................................................................................3 1.2.2 Aquifer types..............................................................................................................................3 1.3 Vertical distribution of groundwater .............................................................................................4 1.4 Groundwater flow systems..............................................................................................................6 2. Fundamental Equations of Groundwater Flow.......................................................................................9 2.1 Darcy's Law......................................................................................................................................9 2.2 Generalization of Darcy's Law......................................................................................................13 2.3 Equation of continuity ...................................................................................................................15 2.4 Basic equations for steady incompressible flow...........................................................................17 2.5 Basic equations for non-steady compressible flow ......................................................................18 3. Steady Groundwater Flow in Aquifers...................................................................................................23 3.1 Groundwater flow in a confined aquifer......................................................................................23 3.1.1 Conceptual hydrogeological model..........................................................................................23 3.1.2 Mathematical model.................................................................................................................23 3.1.3 Analytical solution ...................................................................................................................24 3.1.4 Analysis of solution..................................................................................................................25 3.2 Groundwater Flow in an Unconfined Aquifer.............................................................................27 3.2.1 Conceptual hydrogeological model..........................................................................................27 3.2.2 Mathematical model.................................................................................................................27 3.2.3 Analytical solution ...................................................................................................................28 3.2.4 Analysis of solution..................................................................................................................29 3.3 Groundwater flow in a semi-confined aquifer.............................................................................32 3.3.1 Conceptual hydrogeological model..........................................................................................32 3.3.2 Mathematical model.................................................................................................................32 3.3.3 Analytical solution ..................................................................................................................33 3.3.4 Analysis of result......................................................................................................................34 4. Steady Groundwater Flow to Wells ........................................................................................................37 4.1 Groundwater flow to a well in a confined aquifer.......................................................................37 4.1.1 Conceptual hydrogeological model..........................................................................................37 4.1.2 Mathematical model.................................................................................................................37 4.1.3 Analytical solution ...................................................................................................................39 4.1.4 Analysis of results....................................................................................................................40 4.1.5 Application to pumping test .....................................................................................................41 4.2 Groundwater flow to a well in an unconfined aquifer ................................................................43 4.2.1 Conceptual hydrogeological model..........................................................................................43 4.2.2 Mathematical model.................................................................................................................43 4.2.3 Analytical solution ...................................................................................................................44 4.2.4 Analysis of results....................................................................................................................46 4.2.5 Application to pumping test .....................................................................................................46 4.3 Groundwater flow to a well in a semi-confined aquifer..............................................................48 4.3.1 Conceptual hydrogeological model..........................................................................................48 4.3.2 Mathematical model.................................................................................................................48 4.3.3 Analytical solution ...................................................................................................................49 1
4.4 Methods of superposition and images 4.4.1 Method of superposition 44.2 Method of images 4.5 Flow net…… 4.5.1 Potential function and equipotential lines 4.5.2 Stream function and stream lines 4.5.3 Flow net 5. Non-Steady Groundwater Flow in Aquifers 5.1 Basic equations for non-steady flow in aquifers. 5.1.1 Confined aquifer 5.2 Non-steady Groundwater Flow in a confined aquifer. 5.2.1 Conceptual hydrogeological model 5.2.2 Mathematical model 5.2.3 Analytical solution 76 5.2. 4 Analysis of the resul .3 Non-steady Groundwater Flow in an unconfined aquifer 5.3.1 Conceptual hydrogeological model 78 5.3.2 Mathematical model 78 5.3.3 Analytical solutions 5.3.4 Analysis of results 6. Non-steady Groundwater Flow to wells 6.1 Groundwater flow to a well in a confined aquifer 6.1.1 Conceptual hydrogeological model 6.1.2 Mathematical model 6.1.3 Analytical Solution: Theis formula(1935) 6. 1. 4 Analysis of the solution 86 6. 1. 5 Simplification of Theis formula: Jacob's formula 6.1.6 Applications 6.2 Non-steady groundwater to a well in an unconfined aquifer. 6.2.1 Conceptual hydrogeological model 6.2.2 Mathematical model 6.2.3 Analytical Solution 96 6.2.5 Application of the solution 3 Non-steady groundwater flow to a well in a semi-confined aquifer 6.3.1 Conceptual hydrogeological model 6.3.2 Mathematical model 6.3.3 Analytical solution 6.3.4 Analysis of the results 6.3.5 Application of the solution 7. Refe 8. Anneres T1 Well function of confined aquifers T2 Well function of semi-confined aquifers 12 T3 Function e Ko(x)…., T 4 Function Io(x),I, (x), Ko(x), K(x) 114 9. Exercise
4.4.4 Analysis of results ................................................................................................................... 52 4.4 Methods of superposition and images.......................................................................................... 55 4.4.1 Method of superposition.......................................................................................................... 55 4.4.2 Method of images.................................................................................................................... 61 4.5 Flow net .......................................................................................................................................... 65 4.5.1 Potential function and equipotential lines................................................................................ 65 4.5.2 Stream function and stream lines............................................................................................. 66 4.5.3 Flow net................................................................................................................................... 66 5. Non-steady Groundwater Flow in Aquifers........................................................................................... 71 5.1 Basic equations for non-steady flow in aquifers.......................................................................... 71 5.1.1 Confined aquifer...................................................................................................................... 71 5.1.2 Unconfined aquifer.................................................................................................................. 72 5.2 Non-steady Groundwater Flow in a confined aquifer ................................................................ 75 5.2.1 Conceptual hydrogeological model ......................................................................................... 75 5.2.2 Mathematical model ................................................................................................................ 75 5.2.3 Analytical solution................................................................................................................... 76 5.2.4 Analysis of the result ............................................................................................................... 77 5.3 Non-steady Groundwater Flow in an unconfined aquifer ......................................................... 78 5.3.1 Conceptual hydrogeological model ......................................................................................... 78 5.3.2 Mathematical model ................................................................................................................ 78 5.3.3 Analytical solutions................................................................................................................. 79 5.3.4 Analysis of results ................................................................................................................... 81 6. Non-steady Groundwater Flow to Wells................................................................................................ 83 6.1 Groundwater flow to a well in a confined aquifer ...................................................................... 83 6.1.1 Conceptual hydrogeological model ......................................................................................... 83 6.1.2 Mathematical model ................................................................................................................ 84 6.1.3 Analytical Solution: Theis formula (1935).............................................................................. 85 6.1.4 Analysis of the solution ........................................................................................................... 86 6.1.5 Simplification of Theis formula: Jacob's formula.................................................................... 87 6.1.6 Applications............................................................................................................................. 87 6.2 Non-steady groundwater to a well in an unconfined aquifer..................................................... 94 6.2.1 Conceptual hydrogeological model ......................................................................................... 94 6.2.2 Mathematical model ................................................................................................................ 94 6.2.3 Analytical Solution.................................................................................................................. 96 6.2.4 Analysis of results ................................................................................................................... 97 6.2.5 Application of the solution ...................................................................................................... 98 6.3 Non-steady groundwater flow to a well in a semi-confined aquifer .......................................... 99 6.3.1 Conceptual hydrogeological model ......................................................................................... 99 6.3.2 Mathematical model .............................................................................................................. 100 6.3.3 Analytical solution................................................................................................................. 101 6.3.4 Analysis of the results............................................................................................................ 102 6.3.5 Application of the solution .................................................................................................... 104 7. References............................................................................................................................................. 110 8. Annexes................................................................................................................................................. 111 T.1 Well function of confined aquifers............................................................................................. 111 T.2 Well function of semi-confined aquifers.................................................................................... 112 T.3 Function e K (x) 0 x ..................................................................................................................... 113 T.4 Function I (x), I (x) 0 1 , K (x), K (x) 0 1 ...................................................................................... 114 9. Exercises............................................................................................................................................... 116 2
9.1 Fundamental Equations of Groundwater Flow I16 9.2 Steady groundwater Flow in Aquifers 117 9.3 Steady groundwater Flow to wells 9.4 Non-steady groundwater Flow to Wells 127
9.1 Fundamental Equations of Groundwater Flow.........................................................................116 9.2 Steady Groundwater Flow in Aquifers ......................................................................................117 9.3 Steady Groundwater Flow to Wells............................................................................................120 9.4 Non-steady Groundwater Flow to Wells....................................................................................127 3
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1. Introduction 1.1 Hydrological Cycle a schematic view of the global hydrologic cycle is shown in Figure 1. 1. This diagram shows the interactions and mass transfers (water in different states) that occur between the atmosphere land surfaces and oceans "气 只z"z月0 Figure 1 SChematic diagram of hydrologic cycle(from Bear and Verruijt, 1987)
1. Introduction 1.1 Hydrological Cycle A schematic view of the global hydrologic cycle is shown in Figure 1.1. This diagram shows the interactions and mass transfers (water in different states) that occur between the atmosphere, land surfaces, and oceans. E T = Evapotranspiration; E = Evaporation; I = Infiltration; SR = Surface runoff; R F = Return flow from irrigation; N = Natural replenishment. Figure 1.1Schematic diagram of hydrologic cycle (from Bear and Verruijt, 1987) 1
Atmospheric water and solar energy provide the main inputs for the generation of precipitation, which falls over the land and oceans. Rainfall can either infiltrate into the soil system, percolate to deeper ground water, evaporate or transpire through vegetation back to the atmosphere, or run into the nearest streams or rivers. Infiltrating water is the main source of recharge to the root zone and groundwater aquifers below. Rivers can also recharge aquifers or can act as discharge points for aquifer outflows. The ocean is the ultimate receptor of surface and groundwater contributions from surrounding land masses and provides the main source of water for evaporation back to the atmosphere Table 1. 1 shows the distribution of water throughout the earth. Clearly, the oceans and icecaps dominate as sources of water Table 1.1 Distribution of worlds estimated water resources Location Surface w ater Percentage Equivalent Residence area (km) Volume of total (% depth(m) ti x10° (km)x 10 Surface water Lakes and1.55 0.13 0.01 0.25 reservoirs Swamps <0.1 <0.01 007 years River channels <0.1 01 <0.01 0.003 2 weeks Subsurface water Soil moisture 130 0.07 0.01 Groundwater 130 10,000 years Icecaps and 17.8 10-1000 glaciers year Atmosphere 504 0.01 0.025 10 days Oceans and 361 1370 2500 4000 years seas Total 1460 100 2680 According to these figures, the present amount of free water on earth equals 1460 million km corresponding to a layer 2680 m thick over the whole earth surface. It seems that the supply of water on earth is nearly inexhaustible. However, a completely different picture obtained when water qual ity is taken into account Of the total amount of free water in earth, more than 94% is salt water. which cannot be used for agriculture or for domestic and industri consumption. The water present as snow or ice(2%), and as water vapour in the atmosphere (.001%), cannot be used for these purposes either, and so, for the use of our society only the
Atmospheric water and solar energy provide the main inputs for the generation of precipitation, which falls over the land and oceans. Rainfall can either infiltrate into the soil system, percolate to deeper ground water, evaporate or transpire through vegetation back to the atmosphere, or run into the nearest streams or rivers. Infiltrating water is the main source of recharge to the root zone and groundwater aquifers below. Rivers can also recharge aquifers or can act as discharge points for aquifer outflows. The ocean is the ultimate receptor of surface and groundwater contributions from surrounding land masses and provides the main source of water for evaporation back to the atmosphere. Table 1.1 shows the distribution of water throughout the earth. Clearly, the oceans and icecaps dominate as sources of water. Table 1.1 Distribution of World's estimated water resources Location Surface area (km2 ) x 106 Water Volume (km3 ) x 106 Percentage of total (%) Equivalent depth (m) Residence time Surface water Lakes and reservoirs 1.55 0.13 <0.01 0.25 -10 years Swamps <0.1 <0.01 <0.01 0.007 1-10 years River channels <0.1 <0.01 <0.01 0.003 -2 weeks Subsurface water Soil moisture 130 0.07 < 0.01 0.13 2 weeks – 1 year Groundwater 130 60 4 120 2 weeks – 10,000 years Icecaps and glaciers 17.8 30 2 60 10 – 1000 years Atmosphere 504 0.01 <0.01 0.025 -10 days Oceans and seas 361 1370 94 2500 -4000 years Total 1460 100 2680 Source: Nace, 1971 According to these figures, the present amount of free water on earth equals 1460 million km3 corresponding to a layer 2680 m thick over the whole earth surface. It seems that the supply of water on earth is nearly inexhaustible. However, a completely different picture obtained when water quality is taken into account. Of the total amount of free water in earth, more than 94% is salt water, which cannot be used for agriculture or for domestic and industrial consumption. The water present as snow or ice (2%), and as water vapour in the atmosphere (.001%), cannot be used for these purposes either, and so, for the use of our society only the 2
remaining 4% fresh liquid water is available. It will be clear from this figure that the development of worlds economy must rely on fresh water resources. The storage of fresh water on earth consists mainly of groundwater. Even if we consider only the most active groundwater storage, 4 million km instead of 60 million km, groundwat still accounts for 95%, the surface water in rivers and lakes accounts only 3. 5 of the total quantity and is most vulnerable to pollution. On the other hands, groundwater more homogeneous and stable spatial and temporal distribution and good quality. In the future, people will rely more and more on groundwater for water supply 1.2 Aquifer systems 1. 2.1 Aquifer, aquitard, and aquiclude Groundwater is stored in geological formations. According to the volume of storage and capacity of transmitting water, geological formations are distinguished relatively as aquifer aquitard and aquiclude An aquifer is defined as a saturated permeable geological unit that stores a big quantity of water and is permeable enough to yield economic quantities of water to wells. The most common aquifers are unconsolidated sand and gravel, but permeable sedimentary rocks such as sandstone and limestone and heavily fractured can also be classified as aquifers An aquitard is a geological unit that is permeable enough to transmit water in significant quantities when viewed over large areas and long periods, but its permeability is not sufficient to justify production wells being placed in it. Clays, loams and shale are typical aquitards An aquiclude is an impermeable geological unit that dose not transmit water at all. Dense unfractured igneous or metamorphic rocks are typical aquicludes. In nature, truly permeable geological units seldom occur; all of them leak to some extent, and must therefore be classified as aquitards. In practice, however, geological units can be classified as aquicludes when their permeability is several orders of magnitude lower than that of an overlying or underlying aquifer 1.2.2 Aquifer types There are three main types of aquifer: confined, unconfined and semi-confined aquifers (Figure 1. 2)
remaining 4% fresh liquid water is available. It will be clear from this figure that the development of world's economy must rely on fresh water resources. The storage of fresh water on earth consists mainly of groundwater. Even if we consider only the most active groundwater storage, 4 million km3 instead of 60 million km3 , groundwater still accounts for 95%, the surface water in rivers and lakes accounts only 3.5 % of the total quantity and is most vulnerable to pollution. On the other hands, groundwater is of more homogeneous and stable spatial and temporal distribution and good quality. In the future, people will rely more and more on groundwater for water supply. 1.2 Aquifer systems 1.2.1 Aquifer, aquitard, and aquiclude Groundwater is stored in geological formations. According to the volume of storage and capacity of transmitting water, geological formations are distinguished relatively as aquifer, aquitard and aquiclude. An aquifer is defined as a saturated permeable geological unit that stores a big quantity of water and is permeable enough to yield economic quantities of water to wells. The most common aquifers are unconsolidated sand and gravel, but permeable sedimentary rocks such as sandstone and limestone, and heavily fractured or weathered volcanic and crystalline rocks can also be classified as aquifers. An aquitard is a geological unit that is permeable enough to transmit water in significant quantities when viewed over large areas and long periods, but its permeability is not sufficient to justify production wells being placed in it. Clays, loams and shale are typical aquitards. An aquiclude is an impermeable geological unit that dose not transmit water at all. Dense unfractured igneous or metamorphic rocks are typical aquicludes. In nature, truly impermeable geological units seldom occur; all of them leak to some extent, and must therefore be classified as aquitards. In practice, however, geological units can be classified as aquicludes when their permeability is several orders of magnitude lower than that of an overlying or underlying aquifer. 1.2.2 Aquifer types There are three main types of aquifer: confined, unconfined, and semi-confined aquifers (Figure 1.2). 3
Confined aquifer A confined aquifer(Figure 1. 2A)is bounded above and below by an aquiclude. In aquifer, the pressure of the water is usually higher than that of the atmosphere, so that if a well taps the aquifer, the water in the well rises above the top of the aquifer, or even above the ground surface. The aquifer then is called artesian aquifer Unconfined aquifer n unconfined aquifer(Figure 1. 2B), also known as a phreatic aquifer, is bounded below by an aquiclude but is not restricted by any confining layer above it. Its upper boundary is the water table, which is free to rise and fall. Water in a well penetrating an unconfined aquifer is at atmospheric pressure and does not rise above the water table Semi-confined aquifer A semi-confined aquifer(Figure 1.2C and D), also known as a leaky aquifer is an aquifer whose upper and lower boundaries are aquitards or one boundary is an aquitard and the other is an aquiclude. Water is free to move through the aquitards, either upward or downward. If a leaky aquifer is in hydrological equilibrium, the water level in a well tapping it may coincide with the water table. The water level may also stand above or below the water table depending on the recharge and discharge conditions In deep sedimentary basins, an interbedded system of permeable and less permeable layers that form a multi-layered aquifer system(Figure 1. 2E), is very common. But such an aquifer system is more a succession of leaky aquifers, separated by aquitards, rather than a main aquifer type 1.3 Vertical distribution of groundwater The vertical distribution of groundwater may generally be categorized zones of aeration and saturation(Figure 1.3). The saturated zone is one in which all voids are filled with water under hydrostatic pressure. In the zone of aeration, the interstices are filled partly with air, partly with water. The saturated zone is commonly called the groundwater zone. The zone of aeration may ideally be subdivided into several sub zones. Todd classifies these as follow Soil water zone A soil water zone begins at the ground surface and extends downward through the major root band. Its total depths are variable and dependent on soil type and vegetation. The zone unsaturated except during periods of heavy infiltration. Three categories of water classification may be encountered in this region: hygroscopic water, which is adsorbed from the air; capillary water, held by surface tension; and gravitational water, which is excess soil water draining through the soil
Confined aquifer A confined aquifer (Figure 1.2A) is bounded above and below by an aquiclude. In aquifer, the pressure of the water is usually higher than that of the atmosphere, so that if a well taps the aquifer, the water in the well rises above the top of the aquifer, or even above the ground surface. The aquifer then is called artesian aquifer. Unconfined aquifer An unconfined aquifer (Figure 1.2B), also known as a phreatic aquifer, is bounded below by an aquiclude, but is not restricted by any confining layer above it. Its upper boundary is the water table, which is free to rise and fall. Water in a well penetrating an unconfined aquifer is at atmospheric pressure and does not rise above the water table. Semi-confined aquifer A semi-confined aquifer (Figure 1.2C and D), also known as a leaky aquifer is an aquifer whose upper and lower boundaries are aquitards, or one boundary is an aquitard and the other is an aquiclude. Water is free to move through the aquitards, either upward or downward. If a leaky aquifer is in hydrological equilibrium, the water level in a well tapping it may coincide with the water table. The water level may also stand above or below the water table, depending on the recharge and discharge conditions. In deep sedimentary basins, an interbedded system of permeable and less permeable layers, that form a multi-layered aquifer system (Figure 1.2E), is very common. But such an aquifer system is more a succession of leaky aquifers, separated by aquitards, rather than a main aquifer type. 1.3 Vertical distribution of groundwater The vertical distribution of groundwater may generally be categorized zones of aeration and saturation (Figure 1.3). The saturated zone is one in which all voids are filled with water under hydrostatic pressure. In the zone of aeration, the interstices are filled partly with air, partly with water. The saturated zone is commonly called the groundwater zone. The zone of aeration may ideally be subdivided into several sub zones. Todd classifies these as follows. Soil water zone A soil water zone begins at the ground surface and extends downward through the major root band. Its total depths are variable and dependent on soil type and vegetation. The zone is unsaturated except during periods of heavy infiltration. Three categories of water classification may be encountered in this region: hygroscopic water, which is adsorbed from the air; capillary water, held by surface tension; and gravitational water, which is excess soil water draining through the soil. 4
